Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 20. #90946 | C4 | semidirect |
| 120. Dic15 | Q32 | semidirect |
| 211. C3×C5 | C4×Q32 | semidirect |
| 241. C5 | #69207 | semidirect |
| 251. C3 | #10600000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11747886 | 2 |
| #11747883 | 2 |
| C2×#90946 | 2 |
| C16×Dic15 | 2 |
| C5×#4503 | 2 |
| C3×#64723 | 2 |
| #11745940 | 2 |
| #10600000 | 3 |
| #69207 | 5 |